The components of the vector 𝑢 are
negative two, one as the terminal point of the vector is negative two units right
(two units left) of the initial point and one unit up from the initial point. What are the components of the
A vector on a coordinate grid
describes how to move from one point to another. The starting point of the vector is
called the initial point. And the endpoint is called the
terminal point. The arrow on the vector’s length
indicates the direction of the vector. We’re travelling from the initial
point to the terminal point.
Vectors in two dimensions have two
components. The first describes the horizontal
movement to get from the initial point to the terminal point. And the second describes the
vertical movement. We define the positive direction to
be to the right for horizontal movements and up for vertical movements.
We’ve been given the components of
the vector 𝑢 then negative two, one. And the explanation is that the
terminal point of this vector is negative two units right and one unit up from the
initial point. We can see this on the diagram. Notice that negative two units
right means the same as two units left.
Now, let’s have a look to the
vector 𝑣. Its initial point is here. And the horizontal and vertical
movements have been marked in for us using orange dotted lines. We can see that, to get from the
initial point to the terminal point, the horizontal movement is to the left, which
means it’s going to be a negative number. Let’s count how many units we need
to move, one, two, three, four, five. So we need to move five units to
the left, which we can write as negative five units to the right. So the first component of our
vector 𝑣 is negative five.
Now, let’s look at the vertical
component. And we can see that we have to move
up to get from our initial point to the terminal point. So we’re going to have a positive
value. Let’s count how many squares we
need to move, one, two, three. If we need to move three units up,
then the vertical component of our vector 𝑣 will be three, positive three, because
up is the positive direction.
We found then that the components
of the vector 𝑣 are negative five, three.